Question

the box plot below shows the number of hours students studied for the last exam. use this boxplot below to answer the following question.

0 1 3 8 15
0 5 10 15
hours studied
a. what is the shape of the distribution of this data?
skewed left skewed right
uniform bell - shaped
b. what percentage of students studied between 3 and 8 hours?
%
c. what is the median for this data?
hours
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Explanation:

Step1: Determine the shape of the distribution

In a box - plot, if the whisker on the right side is longer than the whisker on the left side, the distribution is skewed right. Here, the right - hand whisker (from \(Q_3 = 8\) to \(max=15\)) is longer than the left - hand whisker (from \(min = 1\) to \(Q_1=3\)).

Step2: Calculate the percentage of students between 3 and 8 hours

In a box - plot, the inter - quartile range (\(IQR\)) is from \(Q_1\) to \(Q_3\). The percentage of data within the \(IQR\) is \(50\%\). Here, \(Q_1 = 3\) and \(Q_3=8\), so the percentage of students who studied between 3 and 8 hours is \(50\%\).

Step3: Find the median

The median (\(Q_2\)) is represented by the line inside the box in a box - plot. Here, the median \(Q_2 = 3\) hours.

Answer:

a. Skewed right
b. \(50\)
c. \(3\)